Execution context remains the same on every route change

[eokoneyo]

Kibana version: main (8.15)

Describe the bug:

This issue was reported by on slack, it seems the pageName in the execution context remains the same on every route change. Ideally the on route change the we should set the values of the execution, this typically includes pageName, alongside couple of other values. On investigating this it seems the implementation to gather the details for the current page's context does exist, however it doesn't get persisted to the execution context instance because it's also undefined within said implementation, hence why subscribers receive a stale value

Steps to reproduce:

1. Open up the use_execution_context.ts file, add in the following

   console.log('executionContext:: %o , context to update:: %o \n', executionContext, context);

2. on navigating through pages in app, we'll consistently notice that the value for execution context instance is undefined, with context value actually updating.

Expected behavior:

• Context value computed on route change should be persisted to the execution context instance of the app

[elasticmachine]

Pinging @elastic/appex-sharedux (Team:SharedUX)